How Different is C_Prob, Really?
/In the previous blog we looked at MatterOfStats' new Margin Predictor, C_Marg, and quantified just how different it was from each of the other Margin Predictors. Today I'm going to do the same thing for another of the predictors that's based on the ChiPS Team Rating System, C_Prob.
Where C_Marg provides predictions about home team margins, C_Prob provides home team probability assessments but, since these are also numeric, the same techniques that we used to analyse C_Marg's distinctiveness can also be used for C_Prob's.
Firstly then, as in the previous blog, let's look at the manhattan distance matrix for all pairs of Head-to-Head Probability Predictors.
(In this table and in the chart that follows, WP_Mean is the Probability Predictor more commonly referred to as WinPred, PP_Mean is ProPred, and H2H_Mean is the H2H Unadjusted Probability Predictor.)
I've shown the distances here as percentage point differences. So, for example, the first entry tells us that WinPred (WP_Mean) has this season provided probability assessments that have differed, on average, from Bookie_LPSO's by 10.1 percentage points.
C_Prob, it's clear, likes to keep its distance from the other Probability Predictors, especially H2H, WinPred and ProPred from which, on average, C_Prob's assessment differ by over 12 percentage points per prediction.
The three most directly Bookmaker-derived Predictors tend to differ only very slightly from each other - on average by only 1 or 2 percentage points. ProPred, WinPred and H2H appear to form another, less closely knit, enclave of opinion.
All of this divergence and similarity can be seen in the following chart on which are plotted all of the Predictors using the first two principal coordinates of the distance matrix.
It's cold and lonely in C_Prob town, population 1.
